How can I calculate the rate of decay of a radioactive element?
The decay of a radioactive element is a random process which is governed by the laws of chance.
The rate of decay only depends on the number of undecayed atoms.
This means that the more atoms of a radioactive element you have in your sample, the more chance a decay event will occur in that sample.
This is a 1st order process (which you may have met if you have studied chemical kinetics) for which:
The minus sign shows N is decreasing with time
We can write this as:
A process like this follows exponential decay which means that the time taken for half the original sample to decay is a constant.
This is termed the half - life or
Here is an example for the decay of carbon - 14:
It can be shown that
Let's see how we can use this to calculate the rate of decay from this example:
"What is the rate of decay of 1.00g of radon - 224 which has a half - life of 55s?"
Rearranging we get:
(I have used grams and not atoms as these are proportional and is reflected in the answer's units.)